Impurity temperature screening in stellarators close to quasisymmetry

Abstract

Impurity temperature screening is a favourable neoclassical phenomenon involving an outward radial flux of impurity ions from the core of fusion devices. Quasisymmetric magnetic fields lead to intrinsically ambipolar neoclassical fluxes that give rise to temperature screening for low enough $\unicode[STIX]{x1D702}^{-1}\equiv d\ln n/d\ln T$ . In contrast, neoclassical fluxes in generic stellarators will depend on the radial electric field, which is predicted to be inward for ion-root plasmas, potentially leading to impurity accumulation. Here, we examine the impurity particle flux in a number of approximately quasisymmetric stellarator configurations and parameter regimes while varying the amount of symmetry breaking in the magnetic field. For the majority of this work, neoclassical fluxes have been obtained using the SFINCS drift-kinetic equation solver with electrostatic potential $\unicode[STIX]{x1D6F7}=\unicode[STIX]{x1D6F7}(r)$ , where $r$ is a flux-surface label. Results indicate that achieving temperature screening is possible, but unlikely, at low-collisionality reactor-relevant conditions in the core. Thus, the small departures from symmetry in nominally quasisymmetric stellarators are large enough to significantly alter the neoclassical impurity transport. A further look at the magnitude of these fluxes when compared to a gyro-Bohm turbulence estimate suggests that neoclassical fluxes are small in configurations optimized for quasisymmetry when compared to turbulent fluxes.

Measures of quasisymmetry for stellarators

“…Overall, for these ‘quasisymmetric’ configurations, the QS cost functions appear not to be good indicators of their transport levels. Similar behaviour has been observed in previous studies of quasisymmetric configurations (Martin & Landreman 2020).…”

The DESC stellarator code suite Part 3: Quasi-symmetry optimization

“…The DESC optimization targeting the triple product metric, which converged to a result farther away in parameter space from the other solutions, achieved nearly an order of magnitude better confinement than the others according to these measures. This lack of correlation supports previous claims that quasi-symmetry is not an accurate indicator of transport levels (Martin & Landreman 2020; Rodriguez et al 2022). The triple product quasi-symmetry measure is the only one that does not depend on equilibrium conditions, and this independence from the force balance constraints could aid the optimization process.…”

The DESC Stellarator Code Suite Part III: Quasi-symmetry optimization

“…The DESC optimization targeting the triple product metric, which converged to a result farther away in parameter space from the other solutions, achieved dramatically larger improvements than the others. This lack of correlation supports previous claims that quasi-symmetry is not an accurate indicator of transport levels 24,27 . The triple product quasi-symmetry measure is the only one that does not depend on equilibrium conditions, and this independence from the force balance constraints could aid the optimization process.…”

“…This example shows the QuasisymmetryTwoTerm function corresponding to f C , targeting quasi-helical symmetry. It is also normalized using the same denominator as (27). The syntax for the objective functions QuasisymmetryBoozer and QuasisymmetryTripleProduct corresponding to f B and f T , respectively, are similar.…”